Short Answer
Any one with a need to know or access
Discussion
Any person in the chain of command or administrative person in the execution of their duties may have or be granted access to your counseling packet.
This access may be for the purpose of reviewing the packet for proper counseling, evaluating you for advancement, separation, consideration of an Article 15, rehab transfer, etc.
However usually these individuals are limited to the person who conducts the counseling, platoon sergeant, platoon leader, 1SG/CDR, and the orderly room clerk that files the document. If the counseling is not forwarded to the orderly room it may simply stay between you and the counselor.